Sentence examples for boundary value equations have from inspiring English sources

To evaluate the performance of the numerical study, the analytical closed-form boundary value equations have been developed using the extended Hamiltonian principle.

Recently, many literature on the boundary value of difference equations have appeared.

Such properties as isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel bases property of a system of root functions of some boundary value problems with transmission conditions and its applications to the corresponding initial boundary value problems for parabolic equations have been investigated in [16 19].

In recent years, positive solutions of boundary value problems for difference equations have been widely studied.

As we know, higher-order boundary value problems for differential equations have received great attention in recent years (see [7 16]).

Boundary value problems of fractional equations have been considered in many papers (see [7 10] and the references therein).

In consequence, the subject of differential equations has received much attention and many results on boundary value problems of differential equations have been reported.

In several papers various types of boundary value problems for difference equations have been studied and the monotone iterative method has been applied.

On the other hand, impulsive boundary value problems for differential equations have become an important area of investigation in recent year.

Furthermore, several kinds of the high-order boundary value problems of fractional equations have been studied; see [6 10, 28 31] for example.

The boundary value problems for elliptic equations have been studied extensively by many authors (see, e.g., [1, 2] and the references therein).